This ban basically means that they aren't allowed to use gender neutral terms in schools and state offices. So because in German literally everything is gendered and things like job titles and such things are almost always using the male gendered terms there have been efforts to make language more inclusive.

Like for example the German word for teacher is Lehrer, which is the male gendered form of the word(Lehrerin being the female one). So to make it more inclusive/neutral there are a few forms like for example writing it with a so called gender star like this: Lehrer*In or using neutral terms like Lehrpersonal(Teaching staff).

But conservatives think this is destroying the German language, so we get debates and bans around such things here.

Sorry if this makes no sense, somehow this is super hard to describe in English.

Ok, I'm certainly no expert on this, so take this history/opinion, I'm going to present, with a grain of salt.

I will first note that this has become a culture war issue, and that the reason they want to make this into law, is to score points with the anti-woke crowd. So it's just reactionary populist bullshit.

In German, there are three grammatical genders: masculine, feminine, and neutral (articles: der, die, das).

Most nouns have a roughly equal and seemingly random distribution of those genders. Der Fluss (river), die Insel (island), das Meer (ocean).

There is a glaring exception to this: When you turn a verb into a noun, designating "a person who does that", you append -er and the result is masculine: fahren (to drive) → der Fahrer (driver). BUT you can turn that into a feminine form by appending -in: die Fahrerin (female driver).

In common usage, the masculine form is used whenever the driver is male or the driver is of unspecified gender. Also the masculine plural is usually used when talking about a group of people of mixed genders. Feminists, decades ago, started pointing out that this seems rather to assume that the default is male (think for example about man/woman in English, where man is often used meaning "human"), and also that this might subconsciously reinforce gender stereotypes. Importantly, a lot of job titles fit into this category. An electrician is "der Elektriker", possibly reinforcing the idea that electrician is a job for men in people's minds.

So some feminists set out to make the language more inclusive to women. The first that gained traction, mostly in certain parts of academic, feminist, left and left-liberal publications, was the Binnen-I ("FahrerIn", with a capital I), a stand in for "Fahrer oder Fahrerin" (male or female driver). Because this was deemed non-inclusive to non-binary people, this got pushed out by the supposedly more inclusive "Fahrer*in". The * is supposed to designate other genders, like a sort of wildcard character. Nowadays, you more often see Fahrer:in, which looks better and is apparently better for screen readers on computers, which I've heard insert a little pause there. People who take this very seriously will also insert a little pause where the : is when speaking.

These proposals for more inclusive language are not the only ones in existence btw, just the ones that gained some limited mainstream traction. For example, I had a professor who used "die Programmiererin" (the programmer, feminine form) and the pronoun "sie" (she) for a generic programmer of unspecified gender.

Unfortunately, this ":in" or ":innen" suffix does not address all the issues. There are nouns that have more complex feminine forms than just appending -in. For example, physician is "Arzt", the feminine version is "Ärztin", so "Ärzt:in" or "Arzt:in" looks weird, so you got to go "Arzt oder Ärztin". Even more annoyingly, German doesn't have a gender-neutral pronoun like "they", which results in a lot of "er/sie" (he/she). There are more problems like that which I can't recall off the top of my head right now. The result is that this so-called "gendered" writing sometimes creates a lot of added complexity. I'll note that even in most common situations the result is longer and slightly more complex. AFAIK linguists have also complained that applying this consistently is not totally possible.

My opinion: I think this is dead in the water. The extra complexity, inconsistency (think about grading an inconsistent ruleset) and institutional opposition means this has no chance of ever becoming mainstream. I know people vehemently in favor of these proposals for more inclusive language, who themselves do not use it consistently (or even most of the time) when speaking. If even the true believers struggle this much with it, there's no chance this will ever go mainstream. I will also add that the argument that "this is meant to be inclusive to nonbinary people, trust us" is basically the same argument used by the status-quo defenders, who say "this is meant to include women".

Edit: Oh, and this is also important: The extra complexity almost certainly causes issues for people with limited reading comprehension, like immigrants, since the result is more complex and harder to decipher. Language courses are also unlikely to teach any of this, since it's unofficial. There's certainly an argument to be made that doing something that hurts vulnerable groups isn't very compatible with the goal of inclusiveness.